25points for this question given: ab ≅ bc and ao ≅ oc ok − angle bisector of ∠boc find: m∠aok

By applying the theorems of an isosceles triangle and an angle bisector, m<AOK = 135 degrees.

Recall the Theorem of Isosceles Triangle:

We would apply the above stated to solve the problem given.

We know the following:

We can deduce that:

m<AOK = m<AOB + m<BOK

m<AOK = 90 + 45

m<AOK = 135 degrees.

Therefore, by applying the theorems of an isosceles triangle and an angle bisector, m<AOK = 135 degrees.

Learn more here:

link

Taken together, these three facts imply that triangles AOB and COB are congruent (side-side-side congruence postulate).

Now, it's not exactly clear whether A and C lie on the same line (it's possible that the figure is not drawn to scale). If they do, then both angles AOB and COB are right angles, so angle BOK has measure 45º, and so .

the answer is 31.27mph